As far as I can tell, the only dish that has ever held anything approaching an "official" national dish status in South Africa is Bobotie - the UN Women's Organisation  named it South Africa's national dish in 1954! 

It's not a bad compromise, in a country comprising so many cultures, as it reflects our most unique cuisine not found elsewhere in Africa (or the world), namely Cape Malay cuisine.  This gently spiced cuisine grew out of the influence on Cape cooking of slaves, largely from Java and Indonesia, that were brought to the Cape in the 17th century by the Dutch colonisers and who left their mark in Cape kitchens with dishes characterised by sweetly aromatic spices and the use of fruit in meat dishes.

I have posted a great recipe for it on my blog http://www.cooksister.com/2010/01/bobotie-revisited.html which came originally from the Kaapse Tafel traditional restaurant in Cape Town.

Unofficially, however, I don't think anybody will argue with me if I say South Africa's national dish is the braaivleis or barbecue!